Open a new apple account and not lose data

Voicemails will come to both phones only if you are using the same Apple ID, not if you have a Family Sharing plan with different Apple IDs→FAMILY Sharing - Apple Support.

If you want to convert to family sharing and not lose any content:

• Choose one phone as the Family Organizer
• On both phones go to Settings/[Apple ID name]/iCloud and turn on all of the sync switches, then wait for sync to complete; leave the phones connected to power and Wi-Fi to speed up the process.
• On the phone that is NOT the family organizer Go to Settings/[Apple ID name], scroll down if necessary, and tap Sign Out - you will have to enter the password for the account.
• When asked if you want to keep the content that is synced say Yes.
• Create a new Apple ID on that phone.
• Have the family organizer set up as described in the link above, and invite the other user to join.
• Optionally, turn on the sync switches on the non-organizer's iPhone.